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Regular version of the site
Bachelor 2021/2022

Research Seminar "Mathematical and Computational Engineering in Science and Business"

Type: Elective course
Area of studies: Applied Mathematics and Information Science
When: 3 year, 1-4 module
Mode of studies: offline
Open to: students of one campus
Instructors: Vasilii Gromov
Language: English
ECTS credits: 4
Contact hours: 66

Course Syllabus

Abstract

The specialization seminar offers the opportunity to study subjects and sections of mathematical statistics related to the application of differential equations, machine learning, probability theory and mathematical for modeling various solutions of a wide range of theoretical and applied problems. These tasks include modelling of real-world systems using catastrophe theory and self-organization theory. The computational methods used are standard for machine learning: clustering, pattern recognition, dimension reduction. The purpose of the research seminar is to expand the research horizons of students. It is assumed that at the end of the course, the student will be able to prepare a research paper or grant application. To do this, the student will be involved in the following activities: attending classes (it is obligatory), analyzing a large number of sources in a foreign area for the student in order to learn how to highlight mathematical problems in non-mathematical articles, completing part of a group project, preparing presentations and discussion (peer review) of other people's projects and presentations. Prerequisites Knowledge of basic mathematics: analysis, linear algebra, probability theory, - algorithms, programming fundamentals, the ability to understand computational packages
Learning Objectives

Learning Objectives

  • Be able to prepare and conduct a presentation with a report on a scientific topic, as well as conduct an academic discussion on the materials of the report.
  • To be able to independently choose and study modern scientific articles, find relevant literature.
  • Be able to write scientific texts.
Expected Learning Outcomes

Expected Learning Outcomes

  • Be able to prepare and conduct a presentation with a report on a scientific topic, as well as conduct an academic discussion on the materials of the report.
  • Methods for verifying empirical results: hypothesis testing, bootstrap, randomization, etc.
  • Methods of mathematical modeling based on (stochastic) differential equations, probability theory.
  • Modern computational methods used in related fields, in particular, when forecasting time series and solving inverse problems (Fourier analysis, wavelets, regression, SSA, dimension reduction, moving averages, neural networks, filters, etc. - understanding the advantages and disadvantages each of the methods.
  • To be able to independently choose and study modern scientific articles, find relevant literature. Be able to write scientific texts.
Course Contents

Course Contents

  • Invited talks.
Assessment Elements

Assessment Elements

  • non-blocking During module 1 there must be at least one presentation per each group.
  • non-blocking During module 2 there must be at least two presentations per each group.
  • non-blocking During module 3 there must be at least two presentations per each group and a short speech
  • non-blocking During module 4 there must be at least 1 project/coursepaper presenation per each student. The mod
  • non-blocking Control
Interim Assessment

Interim Assessment

  • 2021/2022 4th module
    0.3 * During module 3 there must be at least two presentations per each group and a short speech + 0.2 * During module 4 there must be at least 1 project/coursepaper presenation per each student. The mod + 0.3 * During module 2 there must be at least two presentations per each group. + 0.2 * During module 1 there must be at least one presentation per each group.
Bibliography

Bibliography

Recommended Core Bibliography

  • Ernest P. Chan. (2021). Quantitative Trading : How to Build Your Own Algorithmic Trading Business. Wiley.
  • Gabaix, X., Gopikrishnan, P., Plerou, V., & Stanley, H. E. (2003). A theory of power-law distributions in financial market fluctuations. Nature, 423(6937), 267. https://doi.org/10.1038/nature01624
  • Irene Aldridge. (2013). High-Frequency Trading : A Practical Guide to Algorithmic Strategies and Trading Systems: Vol. 2nd edition. Wiley.
  • Joel Hasbrouck. (2007). Empirical Market Microstructure : The Institutions, Economics, and Econometrics of Securities Trading. Oxford University Press.
  • Mike Elvin. (2004). Financial Risk Taking : An Introduction to the Psychology of Trading and Behavioural Finance. Wiley.

Recommended Additional Bibliography

  • Christopher M. Bishop. (n.d.). Australian National University Pattern Recognition and Machine Learning. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.EBA0C705
  • Vanderplas, J. T. (2016). Python Data Science Handbook : Essential Tools for Working with Data (Vol. First edition). Sebastopol, CA: Reilly - O’Reilly Media. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=nlebk&AN=1425081